## Analysis & PDE

• Anal. PDE
• Volume 6, Number 4 (2013), 973-991.

### Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity

#### Abstract

We consider the incompressible Navier–Stokes equations in a two-dimensional exterior domain $Ω$, with no-slip boundary conditions. Our initial data are of the form $u0=αΘ0+v0$, where $Θ0$ is the Oseen vortex with unit circulation at infinity and $v0$ is a solenoidal perturbation belonging to $L2(Ω)2∩Lq(Ω)2$ for some $q∈(1,2)$. If $α∈ℝ$ is sufficiently small, we show that the solution behaves asymptotically in time like the self-similar Oseen vortex with circulation $α$. This is a global stability result, in the sense that the perturbation $v0$ can be arbitrarily large, and our smallness assumption on the circulation $α$ is independent of the domain $Ω$.

#### Article information

Source
Anal. PDE, Volume 6, Number 4 (2013), 973-991.

Dates
Accepted: 6 August 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.apde/1513731386

Digital Object Identifier
doi:10.2140/apde.2013.6.973

Mathematical Reviews number (MathSciNet)
MR3092735

Zentralblatt MATH identifier
1350.35144

#### Citation

Gallay, Thierry; Maekawa, Yasunori. Long-time asymptotics for two-dimensional exterior flows with small circulation at infinity. Anal. PDE 6 (2013), no. 4, 973--991. doi:10.2140/apde.2013.6.973. https://projecteuclid.org/euclid.apde/1513731386

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